How to convert a octal number with fractional part into decimal number?

To convert a octal number having integer and fractional part into decimal form we have to multiply the integer part
ones place with 80
tens place with 81
hundreds place with 82
ans so on...
and the fractional part
tenths place by 8-1
hundredths place by 8-2
and so on...

Convert octal number 0.01(base 8) into decimal form.

The following table shows the places, octal number and the multipliers for the corresponding places.

place

ones

DecimalPoint

tenths

hundredths

octal

0

.

0

1

multiplier

80

8-1

8-2

= 0x80 + 0x8-1 + 0x8-2
= 0 + 0 + 0.015625
= 0.015625

So, the required decimal number is
0.01(base 8) = 0.015625(base 10)
Alternatively, (0.01)8 = (0.015625)10
Where, (base 10) means the number is in decimal number system and (base 8) means the number is in octal number system.

Convert octal number 7.12172(base 8) into decimal form.

The following table shows the places, octal number and the multipliers for the corresponding places.

So, the required decimal number is
7.12172(base 8) = 10.16(base 10) (approx. value)
Alternatively, (7.12172)8 = (10.16)10 (approx. value)
Where, (base 10) means the number is in decimal number system and (base 8) means the number is in octal number system.